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Learning perspective and view points

Construction of the cone

Fig. 1 Begin by drawing the square in perspective. This time, if we want the cone to have a circular and not an oval base, the base will need to be a square. [?] Draw the diagonals in order to find the centre of the square, and also put in the lines perpendicular to the two sides in the middle as you will need them in a minute. [J’ai besoin des figures ici ]

Fig.2 Draw the ellipse fitting into the square. Notice that the circle touches the square at four points and that it passes at roughly two thirds of the length of each diagonal.

Fig. 3 Raise a vertical in the middle of the left side of the square.

Fig. 4 Insert the diameter of the circle on the left vertical to obtain the height of the apex which would inscribe the cone in a perfect cube. Move this height towards the centre by inserting it on the diameter perpendicular to the visual ray. Put in a point to mark the apex which is now at the vertical of the perspective centre of the circle. Note the that the perspective centre of the circle is not the geometric centre of the ellipse.

Fig. 5 Now draw the tangents to the ellipse which pass by the apex.

Fig. 6 You can add in as many straight lines as you like, starting from the apex and running to the circle situated at the base of the cone. In this way you will be able to divide up the slices of “cake” in a cone.

Fig .7 If you begin your construction on a square seen in frontal perspective, watch out for aberrations due to a wrong choice of position. The most common mistake is failing to switch to angular perspective once the square has moved too much one side. [?]

Think of it this way: when you look straight in front of you, you can’t see an object which is both close and to one side of you. To do so, you have to turn your head and the vanishing point changes.

The resulting deformation is what makes this drawing awkward to the eye.

Fig. 8 This cone is upside down. Here, the precise height of the apex is not given but we may take it that the apex is located on a downward vertical. Notice that there is no prolongation of a diagonal because the square was not exactly at an angle of 45 degrees. From this you may conclude that the two vanishing points are not equidistant from the centre of the cone.